ADVANCED ADVANCED STRUCTURES-SOLID STRUCTURES-SOLID ELEMENTS : CANTILEVER CANTILEVER BEAM *********
Introduction Introduction to FEM The Finite Finite Element Method (FEM) (FEM) is a numerical technique for nding nding approximate approximate solution of partial dierentially equation (PE) as !ell as integral equation" The nite element method is a good good choice for sol#ing partial dierential dierential equations more complicated the domains$ !hen the domains changes$ !hen the desired precision #aries o#er the entire domains$ or !hen the solution lac%s smoothness" The nal element method originated originated from the need for sol#ing complex elasticity and structural analysis in ci#il and aeronautical engineering" Its de#elopment can &e traced &ac% to the !or% &y 'lexander renni%o and ichard *ourant" +hile the approaches used &y the pioneers are dramatically dierent$ they share one essential characteristic, mesh discreti-ation of continuous domains into a set of the su&.domains$ usually called elements" Plate Add Plate:
This option allo!s you to Triangular Triangular or /uadrilateral /uadrilateral plate elements &y connecting existing nodes" To add quadrilateral plate$ select /uad from the su&.menu" For triangular plates$ select Triangle from the su&.menu " The cursor changes to /uad /uad plate or Triangular Triangular Plate shapes" To create ne! elements$ simply clic% on the existing nodes in the right sequence" ' ru&&er &anded area sho!s the &oundary of the plate &eing generated" Set New Plate Attribute:
0imilar to the 1 0et 2e! Mem&er 'ttri&ute3 command in !hich the user is in can dene the property$ property$ material and releases to each ne! plate element as it is created$ has &een introduced" In order to dene the attri&utes for plate element &efore they are created$ go to Ge!etr" → Add Plate → Set New Plate Attribute# from the main menu"
' dialogue &ox !ill prompt for #arious attri&utes of the plate to &e pre. dened" ' summary of a specic attri&utes are dened in the ta&le &elo!"
Butt$ *reate 2e! Property
*reate 2e! Material
*reate 2e! elease
%u$&ti$ Prompts the plate thic%ness dialogue &ox that the thic%ness of the plate at each of the common node can &e dened" ened the #arious material properties of the plate including poison ratio$ modulus of elasticity$ shear modulus$ etc" ene the degree of freedom to &e released at each node of the plate to
the plane stress no in plane rotation or no stiness" Multiple properties$ releases and materials can &e created and sa#ed for future use" To choose from #arious pre.dened types$ simply select the appropriate denition using the 10elect Property3$ 10elect Material3 or the 1Plate elease3 drop.do!n &oxes" For the program to recogni-e the pre.dened attri&utes$ the 1'ssign these attri&utes !hile creating a ne! plates3 chec% &ox must &e chec%ed" 'ny ne! plate element created from here on !ill no! possess these attri&utes" o! to 0%etch Plates, 4" *lic% the plate icon
"
5" 2o! automatically &eam cursor !ill change into plate cursor and nodes in the structure are #isi&le"
6" Plate can dra!n only clic%ing the four node points" 7" 'fter placing the plate$ clic% C!!a$d# menu→ Me!ber Pr'ert" → Plate T(i&)$e##" 2o! the Properties +hole 0tructure dialog &ox appears"
8" *lic% Thic%ness &utton$ no! the Plate Element9 0urface Property dialog &ox appears$ !here you add dierent types of mem&er properties of plate and surface element"
:" Type respecti#e #alue of thic%ness for the plate element" *lic% 'dd &utton" ;" 2o! clic% 0elect menu→ Plate cursor" <" 2o! select the plates and select the radio &utton 'ssign to selected plates and clic% 'ssign &utton"
9"
2o! open the 6 rendering page" =ou can see the Plate !ith dened thic%ness"
0urface Add Surface:
'dding surface is similar to the adding plates !here the plates can &e placed &y clic%ing only 7 node points !hile the surface can &e placed &y clic%ing more than 7 node points" Finally you ha#e to clic% the node point !here you start placing the surface" o! to 'dd surface in the structure, 4" *lic% 'dd 0urface icon or *lic% >eometry menu → 'dd 0urface" 5" 2o! the &eam cursor changes into surface cursor"
6" Place the surface &y clic%ing the node points and nally clic% the node point !here &egin"
7" 's usual dene the property for surface" Type the respecti#e thic%ness #alue for surface mem&er"
8" 2o! 'ssign the mem&er property to the surface &y selecting the surfaces using the surface cursor"
:" 2o! ?pen 6d endering @ie!"
Meshing Meshing is the process of creating a nite element mesh o#er the respecti#e mem&er" The nodes that form the corners of the polygon representing the super A element must already exit on the dra!ing &efore the facility can &e a#ailed" They can &e selected in a sequence and the process launched" Meshing can &e done o#er the plate and surface they can &e classied into t!o are 4" Plate mesh" 5" 0urface mesh" Plate Me#(i$:
This is an utility meant for ta%ing an existing plate element and su&di#iding into a set of smaller elements" *onsequently$ a plate element must already exist on the dra!ing in order for this facility to &e ena&led" Bsing the Plate *ursor$ *lic% the right mouse &utton on the element and select >enerate Mesh" 'lternati#ely select the Ge!etr" !e$u→ Ge$erate Plate Me#(+ If the element &eing meshed is triangular$ the polygonal mesh feature descri&ed in the pre#ious section !ill automatically &ecome acti#ated" If the element is quadrilateral$ the user ha#e to choose &et!een polygonal and quadrilateral meshing" 4" 0elect the plate element$ right clic% in the selected element" 5" *lic% >enerate Plate Meshing" 2o! the Meshing type dialog &ox appears" 6" *hoose the type of meshing$ *lic% Polygonal Meshing and clic% ?C
7" 2o! the ene Mesh egion dialog &ox appears$ user ha#e to dene the &oundary of the meshing surface" *lic% ?C &utton"
8" 2o! the meshing surface is #isi&le$ then apply the plate load and proceed analysis" •
Polygonal Meshing"
•
/uadrilateral Meshing"
Sur,a&e Me#(i$:
0urface meshing is similar to the process of plate meshing" 0ame procedure is follo!ed for the surface meshing" *lic% Ge!etr" !e$u → Ge$erate Plate Me#(+ 2o! select the surface element and pro#ide respecti#e &oundary condition" *lic% ?C &utton" 2o! you get the surface mesh" SOLID ELEMENTS : CANTILEVER BEAM
Data:
Deam type, *antile#er Deam 0pan , 5"m 0ection si-e, 6 x 7mm 0olid modeling
Fig"4 0olid Model of *antile#er Deam 1.Geometry Creation :
2e! Proect
0elect 0pace Bnits,
File 2ameH*onical dome >eometry
un
2ext"
Gength Hmeters ForceHC2
0elect 'dd &eam
Finish"
structure +i-ard 0elect Model Type, 0olid Model
*lic% 0olid Dloc% and dou&le clic% on it" Gength along JH5"m i#ision along JH5 Gength along = H"7 i#ision along =H7 Gength along KH"6
i#ision along KH6
Model =es?%" >o to Geft side #ie! (Top)
'pply Transfer
Fig"5 Geft side #ie! +Pr'ert",
Isometric #ie!
*ommandsMem&er
*onstants ensity *oncrete
Enter #alueH C29m 6 'ssign to @ie!
?%"
*ommandsMem&er *onstants Elasticity *oncrete Enter #alueH C29m 6 assign to @ie!
?%"
*ommandsMem&er *onstants PoissonLs ratio *oncrete Enter #alueH C29m 6 'ssign to @ie!
?%"
.+ Su''rt# :
*lic% 0upport
*reate Fixed 'dd"
ighlight support 5
>o
to Front
#ie!" 0elect Front nodes of the &eam =es
'ssign
to selected nodes
'ssign
*lose
e
select the nodes and change to &eam cursor"
/+ Ladi$ :
Goad enitions *lic% Goad case etails Primary
2um&er
'dd"
4 Goading type, none Title, Goad case 4
'dd
"
*lic% Goad case 4 details
'dd"
Fig" 6 0election for appliying Goad
Fig"7 Isometric #ie! load applying
*lic% 0olid loads
0olid
pressure Goads select face 2um&erHTop
2ode 4H.4C29m5 2ode 5H.4C29m5
2ode 6H.4C29m5 2ode 7H.4C29m 5 irection >='dd" ighlight face 2o" Pressure >= .4 .4 .4 .4
0elect the top
portion of element
#ie!
it in isomeric #ie!
'ssign to #ie!
'ssign =es"
0+ A$al"#i# T"'e:
*lic% 'nalysis9print
2o
print
'dd *lose"
2ote, 0a#e the File &efore un the Program" 1+A$al"#i#,
From Main Menu
N
'nalysis
un
'nalysis one"
2+Re#ult# , >o
to post processing mode" Maximi-e the screen" *lose the ta&le"
Front #ie!
see
the eOected shape"*lic% 'nimation eOection
'pply?%"
esults 0olid stress contour 0olid stress contour Goad case, Goad case 4 0tress Type, 0xx
'pply ?%"
Fig" 8 0tress contour 0xx
Fig" : Isometric #ie! of stress contour 0xx esults 0olid stress contour 0olid stress contour Goad case, Goad case 4 0tress Type, 0yy
'pply ?%"
Fig" ; Isometric #ie! of 0tress 0xy esults 0olid stress contour 0olid stress contour Goad case, Goad case 4
0tress Type, 0--
'pply ?%"
Fig" < Isometric #ie! of stress contour 0-esults 0olid stress contour 0olid stress contour Goad case, Goad case 4 0tress Type, 0xy
'pply ?%"
Fig" Isometric #ie! of stress contour 0xy
Fig"4 Isometric #ie! of Principal stress 04 esults 0olid stress contour 0olid stress contour Goad case, Goad case 4 0tress Type, 0ign @on Mises
Fig"44
'pply ?% *lose"
0ign @on Mises
Fig"45 0ign con#ention of #arious stresses in plates 2ote, 4"2ormal 0tresses, 0xx$ 0yy and 0-5"0hear 0tresses, 0xy$ 0y- and 0-x 6"Principle 0tresses, 04$ 05 and 06 7" @on Mises 0tresses, 0ide
";; Q(04.05)5 (05.06)5 (06.04)5
